Ptolemy's star tables have been mentioned earlier in this series and again early in this episode. What instrument might Ptolemy (or his contemporaries) have used to see the stars?

They observed the stars with their eyes without any aid of magnifying instrument.

Explanation:

Ptolemy or Claudius Ptolemaeus was the Greek astronomer, mathematician, and geographer who proposed the theory named Ptolemaic System. According to this system of belief, the Universe was thought to be 'geocentric.' Meaning that all the planets, Sun and Moon revolves around the Earth; that the Earth was the center of the Universe. He wrote about his ideas in a book called Almagest.

Ptolemy made observations of the geocentric system by observing the Universe and planets with his naked eyes. He did not use any instrument to make these observations. The only planets known at that time were the Mars, Jupiter, Saturn, Mercury, Venus as they were visible with the naked eyes.

So, the correct answer is that Ptolemy or his contemporaries did not use any instrument but based their observations with their naked eyes.